To the surprise of many observers, the 2005 International Comparison Program (ICP) found substantially higher purchasing power parity (PPP) rates, relative to market exchange rates, in most developing countries. For example, China s price level index -- the ratio of its PPP to its exchange rate -- doubled between the 1993 and 2005 rounds of the ICP. The paper tries to explain the observed changes in PPPs. Consistently with the Balassa-Samuelson model, evidence is found of a "dynamic Penn effect," whereby more rapidly growing economies experience steeper increases in their price level index. This effect has been even stronger for initially poorer countries. Thus the widely-observed static (cross-sectional) Penn effect has been attenuated over time. On also taking account of exchange rate changes and prior participation in the ICP s price surveys, 99 percent of the variance in the observed changes in PPPs is explicable. Using a nested test, the World Bank s longstanding method of extrapolating PPPs between ICP rounds using inflation rates alone is out performed by the model proposed in this paper.